Furthermore, the \((1+1)\) -dimensional holographic superconductors
have been developed in the background of BTZ black hole
[1]}. BTZ black hole is the well-known solutions of general
relativity in \((2+1)\) -dimensional spacetime which plays a crucial
role in understanding the gravitational interaction in low
dimensional spacetimes. In order to study the one-dimensional
holographic superconductor one may apply \(AdS_3/CFT_2\) 
correspondence [2]}, [3]}, [4]}, [5]}, [6]}. One-dimensional
holographic \(s\) -wave and \(p\) -wave superconductors were analyzed
both analytically and numerically from different points of view in
(see e.g.
[7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}).
It is worth noting that most investigations on the
\((1+1)\) -dimensional holographic \(p\) -wave superconductors are done
in the framework of linear Maxwell electrodynamics. Therefore, it
is fascinating to study the effects of nonlinearity in such a
holographic superconductor. In the present work, we would like to
extend the investigation on the one-dimensional holographic
superconductor by considering the BI nonlinear electrodynamics
when gauge and vector fields backreact on background geometry. It
is worth noting that the \((1+1)\) -dimensional holographic \(p\) -wave
superconductor is located on the boundary of \((2+1)\)  dimensional
spacetime. While the gauge and the vector fields are defined in
the \((2+1)\) -dimensional BTZ black hole. It is well-known that the
electric field of a point charge in \((2+1)\) -dimension has the form
\(E(r)=q/r\) . Thus, there is still a divergency in the electric
field at the location of point charge (\(r=0\) ). However, taking the
BI electrodynamics into account can remove this divergency as
well. This is the main motivation for investigating the
\((1+1)\) -dimensional holographic \(p\) -wave superconductor in the
presence of nonlinear BI electrodynamics.
